Tuesday, February 26, 2013

"We are like riders on the back of an elephant. We hold the reins and think we are in control; we can steer the elephant as long as the elephant has no desires of its own.

But in the end the elephant does what the elephant wants to do and we are left helplessly raging at our own apparent weakness."

This purports to be a statement about dieting, but what an elegant theory of consciousness and free will in general.

This 'two systems' model also applies to politics. While the people (the elephant) are fed, housed and content, the politicians (the rider) have the illusion they are in control. Heaven help them though when the masses rise in discontented revolt!

I wonder if there's a general theory hiding away here somewhere? (Control Theory in its modern, AI-influenced mode).

My mother is ninety, but that hasn't diminished her interest in all things medical. After talking about 23andMe, she was sent scurrying around the house for old hair brushes. I now have a collection of her hair and some cheek swabs, packaged and ready to be lodged in my safe at home

Twenty years time, when whole-genome sequencing costs five pounds, one of her descendants may be interested in analysing this particular ancestor .. or cloning her!
---
Is it reassuring to have your complete genome on file? In principle you could be cloned in future. That person would be your "future-twin" .. and so immortality beckons.

I don't know: does a twin feel the other twin is a version of themselves? I rather suspect not.

Monday, February 25, 2013

The man from DHL has just delivered the 23andMe sample tube ready for me to spit my DNA (pictured). The instructions for spitting, registering the sample and completing the return DHL label are very complicated. Anyone would think my genetic material was toxic waste!

Update: forms completed and spitting done. The DHL courier will be here Wednesday afternoon and the sample will be in Los Angeles on Friday. Then it's a number of weeks wait for the genotyping report.

Spitting a large amount of fluid is quite hard .. if you don't practice it as a recreational activity!

I have never really engaged with Julian Barnes, to my own loss. "The Sense of an Ending" is short enough to read in a day, but impossible then to put aside in your thoughts. Barnes' protagonist, Tony Webster, is a kind of everyman to those of us who were students at the end of the sixties - and are now in our early sixties.

"By now, The Sense of an Ending by Julian Barnes has gained itself a reputation for being the novel you must read twice. I read it twice, and so did the director of last year’s (2011) Man Booker Prize, which Barnes’ novel won to no surprise.

The book’s plot reads like that of a thriller paperback: full of vengeful ex-girlfriends, youth suicide and illicit sex – though it’s Barnes’ masochistically lyrical insights on loss and memory that drives this novel’s recruiting fan base to keep flipping back the pages.

The book centers on Tony Webster, an Englishman in his sixties, who is unexpectedly bequeathed the diary of Adrian, his childhood friend who had committed suicide forty years earlier. The will is from the late mother of his collegiate ex-girlfriend Veronica. Last he heard from her, she had ditched Tony for Adrian, and was presumably still Adrian’s girlfriend around the time his body was found behind a locked door, bled to death in a bathtub.

Why does Veronica’s mother have Adrian’s diary? And why did she want Tony, of all people, to have it? Tony suddenly finds himself mining his memory to find answers surrounding Adrian’s enigmatic suicide. His search lyrically reveals the weakness of memory as corroboration. These moments, rather than the book’s muscular plot, are where Barnes’ prose is strongest.

“I don’t envy Adrian his death, but I envy him the clarity of his life,” Tony muses in old age. “When you are in your twenties…you can remember your short life in its entirety. Later, the memory becomes a thing of shreds and patches.”

With the patina of hindsight, Tony’s recollection of Adrian reveal memory to be a fractious, fictitious thing, rather than the empirical recount of history in his schoolboy textbooks. What purpose does memory serve outside of corroboration? How does it mold and twist fiction with fact?

In addressing these questions, Barnes’ voice is potently enigmatic when objective details are purposely left out. He spares on physical details as if to shy away from the hard facts that memory can’t provide. The only physical detail we get about any of Tony’s lovers is the way they wear their hair. Dialogue and gossip instead form the basis of what Tony remembers, which makes nearly every conversation doubly interpreted. As Tony says later in life, “All my ‘conclusions’ are reversible.”

Here’s a particularly troublesome scene: in college, Tony asks Veronica why they didn’t have sex until after they broke up. She responds, “I don’t have to answer your questions anymore.”

We can either imagine this the way Tony interprets it: spoken by a curt girl from Britain’s fashionable classes, who dismisses her inferior boyfriend as nothing more than a stepping stone to his smarter, elite friend Adrian.

Or, we can imagine it spoken by an awkward girl with glasses—a misfit in her family, too self-conscious to dance in public—who’s been far too humiliated by the boy to whom she lost her virginity to come up with a clever response. Read the book a second time, and the latter interpretation becomes painfully apparent.

Akin to the nature of memory itself, Barnes’ prose renders these scenes as mere impressions rather than snapshots of a biography. Collectively, those impressions mesh to form something quite far from an objective lens. Nearly every paragraph in this book has multiple interpretations.

Once all the questions are answered, the reader is left in the same state that Tony is in the book’s final pages—floored at life’s essential mysteries, and frustrated that they cannot be relived.

Fortunately for us, we can just read the book again."

---

Perhaps I will. I especially agree with the reviewer about Veronica, who is disparaged by all the other characters as mysterious and impossible, perverse and controlling, on-the-make, a fruitcake.

Yet we sense a greater absence: her story is never told and her life of introverted desperation is something wholly left to the reader to discern. Veronica has been betrayed by everyone.

Sunday, February 24, 2013

This novella of 112 pages tells the tale of Antonio Martens, CID detective turned secret policeman in an unnamed Latin American country. Martens transfers to the "Corps" shortly after the coup, joining the interrogation team as a rookie torturer.

In a parallel development, we meet Enrique Salinas, the student son and heir of Federigo Salinas, who owns a national chain of department stores.

The Colonel has closed the universities and Enrique's vaguely left-wing sentiments drive him to revolt. But the real hard-cases of the resistance want nothing to do with this earnest, bumbling amateur. His worried father concocts an elaborate spoof 'resistance group' to keep his son safe.

The secret police, however, can't fail to notice Enrique's hapless 'subversion'. This spoilt child of the bourgeoisie is soon in the "operating theatre" learning some new realities about life in a police state .. soon to be followed by his father.

The story is told by the torturer Martens in flashback - memoirs written in his prison cell during his trial by the new, more liberal regime. Ironically, the scandal of the treatment of the innocent Salinas appears to have precipitated the very revolution in which they avoided participation.

We are meant, I think, to compare and contrast the trajectories of the Salinas family and Antonio Martens as they head towards their identical doom. But what is in common? It certainly isn't character.

The Salinas family are smart (too smart for their own good) but unforgivably naive. The secret police, by contrast, are thoroughly incompetent and Martens, while not irredeemably evil, is pretty stupid.

Still, while writing in his prison cell, Martens concedes that he has finally understood 'the logic'. When the bureaucracy - any bureaucracy - has you in its grip, it will run the process - 'the logic' - in all its institutional idiocy, never, ever penetrating to the truth.

---

The author, Imre Kertesz, was imprisoned in Auschwitz and Buchenwald and later saw what the Russian Stalinists did to his native Hungary. He was awarded the Nobel Prize for Literature in 2002.

The translator, Tim Wilkinson, has done an excellent job in capturing the different voices in the text.

Saturday, February 23, 2013

"... Gail and Jeremy Bremen are telepaths who met and married ten years ago. Together, they find relief from the psychobabble of voices around them, the minds of people they meet and a larger psychobabble grounded in the whole "wave'' of human intelligence.

When Gail dies of an inoperable tumor behind her eye, Jeremy freaks out, burns down their house, abandons his professorship, and goes on the road.

In Florida, he witnesses a mob murder, is kidnapped by the mob, later escapes.

Taken up by Miz Morgan, a rancher, he finds himself facing razorblade dentures over his important parts and escapes from her too.

In Las Vegas, his mind-reading stands him well at the poker table; he's a huge winner, but the mob is back.

After saving his life still again, he winds up in the hospital, enters the closed-off mind of a retarded blind boy, and finds Gail alive in a probable reality that the boy has put together from particles of Jeremy's mind.

Throughout, in flashback, we are treated to far-out wave-particle theory about a unified wave of human consciousness that allows for transfer of mind or being.

From this description, you might expect a lyrical novel featuring great psychic leaps of imagination.

Simmons leaps, but where he lands in a parallel probability is far less vividly experienced than possibilities allow. The nostalgic opening chapter of 'Summer of Night' is better than this whole novel.

Simmons wrote "The Hollow Man" after publishing his four "Hyperion" novels. He is still plainly fascinated by such Hyperion themes as whether the universe somehow physically encodes realities such as personality, love and consciousness.

Simmons knows enough physics to appreciate that this would mean a common theory for both quantum-mechanics/relativity and consciousness. Hence the novel is full of references to Schrodinger's equation, holography, standing waves, chaos and fractals.

Sadly, this falls into the well-worn SF trap of trying to weave coherent pseudoscience into the plot (Greg Bear commits similar crimes in "Moving Mars").

The "Hyperion Cantos" worked as a beautifully cohesive creation because it merely assumed its universe could be made to work. Like sausage-manufacture, it pays in these circumstances not to look too closely.

Back at "The Hollow Man", if you delete the speculative theorisation there is still an interesting account of the protagonist Jeremy Bremen's descent into American hell.

It's not wholly convincing: Bremen's motivations and actions often don't really make sense and his many escapes from disaster stretch credibility. Still, Simmons is a good-enough writer to keep the pages turning through the bulk of the book.

The final resolution is pretty opaque but makes more sense if you check out 'quantum suicide'.

Friday, February 22, 2013

In the absence of witnesses and reliable forensics, it seems the case against Oscar Pistorius hangs rather heavily on whether he's the nice guy of his public persona or whether he has a dark side: impulsive, aggressive, confrontational, violent.

If the former, the defence could try to put psychological data before the court. I'm not sure whether psychometric tests can be reliably gamed (I imagine that with some coaching, practice and inbuilt-empathy you could simulate most personality-types on a pencil-and-paper test).

MRI scans and genetic profiling, if we understood what we were seeing, seem far more robust.

What if Oscar isn't such a pussycat, and the prosecution arrive with the data.

Defence lawyer: "It was his brain/genes which made my client do it. He had no choice!"

Thursday, February 21, 2013

Signed up on the site, paid my money ... and I'm now awaiting my 'spit kit'.

The Google-associated company 23andMe will then genotype thousands of my genes against their database and will get back to me with a comprehensive health and ancestry report.

Hundreds of diseases are linked with particular alleles (gene variants) on the human genome. Some gene variants make you far more, or less likely to succumb to heart disease, dementia or various forms of cancer. I await my results with interest.

My sudden interest was catalysed by reading Matt Ridley's 1999 book "Genome". The book is dated in a fast-moving field as well as fossilising slightly-obsolete 'nature vs. nurture' confusions while exhibiting the then-current state of political-correctness.

Finally, a bonus shot from a few days ago: my mother on the occasion of her 90th birthday, sharing the event with her robot cat. As proud possessor of an iRobot Roomba, an iPad and WiFi she has been voted 'most digital in the 'hood'.

Friday, February 15, 2013

"In its scientific work, BGI often acts as the enabler of other people’s ideas. That is the case in a major project conceived by Steve Hsu, vice president for research at Michigan State University, to search for genes that influence intelligence. Under the guidance of Zhao Bowen, BGI is now sequencing the DNA of more than 2,000 people—mostly Americans—who have IQ scores of at least 160, or four standard deviations above the mean.

The DNA comes primarily from a collection of blood ­samples amassed by Robert Plomin, a psychologist at King’s College, London. The plan, to compare the genomes of geniuses and people of ordinary intelligence, is scientifically risky (it’s likely that thousands of genes are involved) and somewhat controversial. For those reasons it would be very hard to find the $15 or $20 million needed to carry out the project in the West. “Maybe it will work, maybe it won’t,” Plomin says. “But BGI is doing it basically for free.”

From Plomin’s perspective, BGI is so large that it appears to have more DNA sequencing capacity than it knows what to do with. It has “all those machines and people that have to be fed” with projects, he says. The IQ study isn’t the only mega-project under way. With a U.S. nonprofit, Autism Speaks, BGI is being paid to sequence the DNA of up to 10,000 people from families with autistic children. For researchers in Denmark, BGI is decoding the genomes of 3,000 obese people and 3,000 lean ones."

A lot of people seem to have a problem with the large observed correlation between heredity and IQ (c. 80%). It does tend to undermine the sense that anyone can get 'from log cabin to President'. Still, that's the way Nature works. Clare may come around to this point of view after reading "Genome" by Matt Ridley, which arrived this morning by some Amazon magic.

---

I was once appraised by a senior executive who compared me to my then-boss, A.

"A." he said, "is not particularly good at anything but he is a safe pair of hands. You, by contrast, have both particular strengths and equally particular weaknesses."

I recall that this was a conversation limiting my career prospects.

The strengths he was referring to were intellectual - the normal specificities of an INTP - and were consistent with my then-job as a senior systems architect. The weaknesses ... that's more interesting.

I identify two main personal weaknesses in a corporate context (there is always a context for these discussions) and both are type-weaknesses.

Firstly I am transactional rather than directive. This is not rewarded at senior levels, where they like people to strike out with initiatives, pushing and pulling the organisation along by force of personality. Put another way, corporations tend to like J rather than P in their senior guys and are not big on Taoists.

My other weakness relates to interpersonal skills. I score pretty high on the AQ test and it's interesting to see what this means in practice. As someone whose strength lies in thinking in terms of systems, theories and logical consequences, if someone tells me something I tend to focus on what they actually said and analyse it in logical terms. But humanity is a rather devious species ...

I am quite capable of enlarging my field of view to focus on the actors concerned, their likely motives and the reasons why they might be saying what they do, but it's an additional intellectual act (and unfortunately, I sometimes forget, if what they said was interesting). There are people who schmooze and socialise and manipulate with deft ease - the natural politicians. These too are valued (or make themselves valued) at a senior executive level, but I cannot be that person.

Wednesday, February 13, 2013

This is the title of a book I would like to read (not the American book of this name which already exists and appears to believe the eventual worldwide triumph of 'democracy' is assured).

The book I want to buy and read will be written in the paradigm of sociobiology. It will identify the chief reasons why small-scale and relatively informal governance models which work for tribes or kin-groups, c. 100 strong, don't scale.

Apart from the obvious requirements for hierarchy as the size of a community gets into the tens or hundreds of millions, I would expect a careful treatment of corruption, nepotism and bureaucratisation; the power of vested interests to capture parts of the state and government, the success of populist governments implementing policies which bring a state to ruin, and the abrogation of civilized norms when dealing with out-groups.

Democracy addresses these issues by a careful assignment of limited, but real, power to leadership teams which can be thrown out (almost always against their wills!) by the mass of citizens in a controlled and non-violent process.

Does it work? Not always: it didn't in Chile under Allende, when the policies adopted seemed to be wrecking the economy.

Lenin outlined the soviet model (soviets are elected councils), which on paper creates a form of state which is an organic expression of the self-activity of the masses. What could be more democratic, defined as a state-architecture which genuinely represents the barely-mediated interests of all?

In practice it didn't model the operational arm of Government, the bureaucracy, which in best public choice theory mode promptly took over and transformed the soviets into empty shells. I believe Lenin's architecture here was fundamentally flawed and the outcome inevitable. (Trotskyists disagree .. but comrades, it has actually never worked anywhere, has it?).

Democracy has many bugs but is it really the least bad of all possible architectures? I'm not convinced - we surely have the right conceptual tools now to design credible alternatives - but I still can't seem to find that book on Amazon ...

(Perhaps China will eventually get round to inventing it *wry smile*).

Tuesday, February 12, 2013

Dare I find parallels between the current situation Pope-wise and the final two volumes of Dan Simmons' Hyperion series?

The bureaucracy of the Pax endlessly recycles its malleable machine-politician pope, Lenar Hoyt; this last pope has been a similar, voluntary prisoner of the Vatican bureaucracy. Anyway, enough of that.

In his lead character Aenea's teaching, Simmons points out that the Buddha never taught the reincarnation of the self or soul. Googling (Buddha teachings on reincarnation) confirms this. The Buddha appeared to believe that consciousness, the self, is recreated moment-by-moment as a kind of dynamic standing-wave. An analogy would be a flame.

On death, an enlightened pattern dissipates; one which has not renounced the passions can persist and in some mysterious way inform the life of a subsequent creature .. reincarnation of a kind.

I think this makes more sense if we consider that the meaning of our lives, for good or ill, is the effect they have on our families and communities.

A productive life will help progress our ongoing civilisation; an unproductive life will subtract from it.

This is, of course, so not a new thought - cf. "The sole meaning of life is to serve humanity" - Tolstoy. Recognising our human co-dependence, an evolutionary biologist would agree.

(Everything true about human life is grounded in sociobiology *smile*).

Sunday, February 10, 2013

Over the last two months, despite fasting @ 600 calories three days a week, my weight has plateaued at around 70+ kg. This is a good weight to be at (BMI 22+) so I'll now go back to a two day regime (5:2).

Some of the levelling off I put down to starting gym work-outs three days a week. I expend quite a bit of energy there, including on the resistance machines, and although I couldn't share the same planet as Arnie, there is nevertheless some visible increase in muscle mass. This extra stuff has been built, and counteracts any decrease in fat weight-wise. My waist size has continued to drop as central flab has disappeared - another encouraging sign.
-----------------------

Saturday, February 09, 2013

Don't be deceived by the quick victories of French special forces over AQIM in Mali. The French will soon find themselves in deep trouble.

The basic problem is that Mali is a hopeless mess verging on a failed state. There are no viable governmental institutions, the government itself is a puppet of the army which is rent with violent divisions and corrupt to the core. Atrocities are common.

The Malian state, such as it is, is ethnically sub-Saharan African. The Tuareg in the desert north are Berbers, the descendants of Mediterranean 'back to Africa' population flows 15,000 years ago. The two groups do not, to put it mildly, get on.

So forget all the talk of 'training the army' and 'elections for a new government within the year': Mali is unfixable. It will take a miracle for the French to fashion any kind of exit strategy which looks like success - on any time scale. On the contrary, they will be pushed to become more involved (and how often have we seen that dynamic!).

Everyone will then hate them, and the quagmire will well and truly be in place. Poor M. Hollande!

About half way through my OU quantum mechanics course I realised I had no idea what was going on. I could perfectly well follow the maths: the problem was that I didn't understand how the entities I was learning about connected to 'reality'. The subject might as well have been magick or theology.

I know I was not the only mystified one.

The trouble is that you need to be well-acquainted with the basic framework of QM before you can get its relationship to physical reality straight (it never ceases to be incomprehensible).

So, safe in the knowledge that it makes no sense, here is my current understanding of the basic mechanisms of quantum mechanics.

The quantum state (aka the wavefunction) is what we study in QM; we are not to suppose that this objectively exists out there in spacetime: mathematically, it lives somewhere else, in Hilbert space.

When we propose to make an observation of a quantum system (for example, the energy level of an electron in an atom) we choose the quantum operator corresponding to the property of interest (energy, momentum, position, etc). Call the operator A and the quantum state psi.

If the state of the quantum system can be written in the form A(psi) then we can also write it as a sum (superposition) of A's eigenfunctions, each multiplied by its specific expansion coefficient and the corresponding eigenvalue.

The eigenvalues are the values of possible observations, and the modulus of their expansion coefficients gives the probability of observing that value.

What does it mean to apply an operator to a quantum state?

Suppose the operator is the Hamiltonian for the infinite square well potential, H. Initially the electron had some prior quantum state - maybe it was a free particle. Applying Schrodinger's equation for the infinite square well case to the quantum state psi is equivalent to putting the electron into the box. So applying the operator defines a constraint upon psi which effectively sets up the experimental situation.

However, once we have registered the observation of a specific eigenvalue, the state vector changes again to the corresponding eigenfunction.

So here, in all its incomprehensibility and weirdness, is the reason why quantum mechanics is so hard to grasp, and why no-one really understands what's going on .. even though it all works so brilliantly in practice.

Friday, February 08, 2013

Galileo believes in the power of reason and the evidence of the senses. Look through his telescope and you will see the phases of Venus and the moons of Jupiter. Proof that not everything in the celestial heavens revolves on crystalline spheres around the Earth.

Today, from a safe historical distance, we mock those Pontifical authorities who refused to look through Galileo's telescope. But they were smart people who knew that matters of faith and public order were far too important to be left to the meddling of naive scientists.

Brecht gives the politically-correct authorities a number of arguments.

1. God created man in his image, He would not have placed him on some small cinder spinning around something else. Plus your views directly contradict scripture, the word of God.

2. You have no good arguments to explain why your version of reality could be correct. (Galileo: "Just look!").

3. If we were to accept your radical reshaping of the cosmos, where heaven has vanished from the skies, the common people would be thrown into insurrectionary chaos.

It's suggested that Galileo's new evidence would be the thin end of a wedge, which would destroy the existing social order: 'Apres moi le deluge'.

Galileo is told quietly: 'You may use your heliocentric theory privately if the maths makes the calculations easier, but don't propose it as a model of reality.'

Thursday, February 07, 2013

I write this at lunchtime from the BHS restaurant which gives an excellent first floor view of the RSC and the Stratford Marina (pictured) - the hot chocolate is good too.

We've arrived at the town centre from Anne Hathaway's cottage, pictured, where it was exceedingly cold, and where we were preceded by a coach-load of French school-students.

Update: pm we watched 'The Winter's Tale', which according to Wikipedia is one of Shakespeare's problem plays. The first three acts (jealous king accuses wife of infidelity with childhood chum .. tragic consequences) is a BBC2-type drama. The last two acts are dominated by big fat people being vulgar and bawdy; also Morris Men. Proper ITV. We found our attention wandering.

Shock! Horror! Clare (and myself) forgot to leave food out for the cat before we left. We thought he'd be gouging the flesh from our very bodies in his starvation as we entered the house.

But no, he'd been perfectly happy with the remnants of his munchy-crunchies ...

Wednesday, February 06, 2013

We're in Stratford-on- Avon to take in a couple of plays. This evening 'The Life of Galileo' by Brecht at the Swan Theatre.

This was a lively, heartfelt performance which showcased reason and science vs. obscurantist arguments from authority designed solely to buttress the interests of those in power. This never fails to be relevant.

Brecht makes Galileo an early Marxist (science must be in the service of the people, not the exploiters) but in truth it's not always obvious how to achieve this desirable end - ask the Party?

Once again, the Catholic Church get to be the bad guys. Has there ever been an honest, non-self-serving, intelligent drama which had Catholics genuinely as good guys?

The QC reported this morning on Mid Staffordshire hospital, which managed to kill hundreds of patients between 2005 and 2008 (and probably since) through negligence.

I hope the learned gentleman had economists on his public enquiry team, because the disaster encapsulated the results of misaligned incentives and unintended consequences.

The management were too busy hitting financial and throughput targets. Success in meeting the regulatory requirements was optimised by abusing the patients.

The example here represents a very generic problem and I think the best framework for analysis actually comes from Artificial Intelligence.

There are two kinds of systems (agents in AI-speak). Those which are intrinsically good (which we like and admire) and bad systems, which we can't trust and which we therefore try to hedge around with regulation.

In AI terms, we'd think of this in terms of an agent in its environment. The environment defines certain beliefs, practices and goals as 'good' and the agent is judged by whether its own beliefs, practices and goals are aligned. Many natural and artificial systems are examples of this general paradigm.

(Notice 'good' and 'bad' are never absolutes but are always relativised to the nature of the environment: this is how to think about ethics.)

In evolution 'good' organisms are adapted to their niches; 'bad' ones are unfit and get culled.

In a capitalist economy, in a competitive market, some companies find their niches and flourish, others go bust.

In both these examples, it's difficult to specify the niche (and therefore to formally specify what counts as 'good') so we throw variation at the niche and see what works: failures are terminated.

Competition and choice: there are public policy lessons here! Most notably regulation is always second best, rarely works well and often doesn't work at all. And more is often less.

Tuesday, February 05, 2013

I now know what a Gateaux differential is, although I see from my textbook annotations that I passed this way three years ago. The prepared mind sees a different world.

In a similar vein, my longtime confusion between expansion coefficients (in some representation) and eigenvalues of the corresponding operator has finally been resolved by re-reading Gary Bowman's excellent 'Essential Quantum Mechanics'.

It's very blowy here and we had considered a walk. Clare is deeply into our recently-purchased guide to 'The Way of St. James', specifically the route along the North Spanish coast. I was able to download an augmented reality app for 'el Camino' which shows the view in front of you (using the camera) on the phone's screen + overlaid Camino information. As our house is not actually on the famed way, all we saw was a blue arrow telling us to turn around on the couch and set off southwards!

I think we'll have some of those enticing scones Clare's currently cooking instead.

Monday, February 04, 2013

I read somewhere that once past elementary arithmetic, all of mathematics can be classified as algebra or geometry.

This is a profound distinction.

Algebra deals in axioms, rules of inference and abstract theorems speaking to a digital, verbal intelligence. Geometry, on the other hand, is the visualisation of shape and space ... and feels kind of analogue.

Algebra inhabits a space near to logic - and you feel it would suit lawyers and computer programmers. Geometry deals in complex, high-dimensional manifolds and would not feel strange to visuo-spatial professionals such as architects, pilots and explorers.

One feels that algebra is a creature of the judgemental left-brain while geometry emerges and grows from the intuitive right-brain.

I have always only understood a mathematical theorem when I can visualise a picture of its underlying shape, a model which makes manifest why the result is, when looked at in the right way, obvious.

But then, I'm an INTP. Let the INTJs and ENTJs wave the flag for algebra!

Sunday, February 03, 2013

I have a fantasy: I'd like to trade my Toyota Auris for a 4x4. Flooded tracks on the Somerset levels, mountain roads across the Mendips glazed with black ice and dusted with driven snow .. I don't care, I've got a 4x4! The Sunday Times'Drive' section today had an article on frugal off-roaders, featuring the putative car of my dreams for less than 18k. Leaving their Mini Countryman option aside as a ludicrous concept, The Times offered the Fiat Panda and the Skoda Yeti.